#290 ⟨a, b | aaababba=1⟩
Properties
- Presentation has sum-of-sides 8
- Infinite non-Abelian group
- Group inverses:
- a-1 = a3d
- b-1 = cbab
- c-1 = d
- d-1 = c
Complete rewriting system
- Reduction order:
- Right-to-left recursive path with deg(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
- Auxiliary generator: aaaa=c
- Auxiliary generator: babb=d
- dc ⇒ 1
- cd ⇒ 1
- ca ⇒ ac
- da ⇒ ad
- a4 ⇒ c
- b2c ⇒ a3bab
- babd ⇒ adb2
- bcba ⇒ cbab
- b2ac ⇒ a3(ba)2
- (ba)2d ⇒ adb2a
- b2a2c ⇒ a3baba2
- baba2d ⇒ adb2a2
- b2a3 ⇒ a3dbcb
- baba3 ⇒ d(bc)2
- bab2 ⇒ d
# ab:aaababba=1 reversed:cda/b aaaa=c,babb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaaa=c
bbc=aaabab
babd=adbb
bcba=cbab
bbac=aaababa
babad=adbba
bbaac=aaababaa
babaad=adbbaa
bbaaa=aaadbcb
babaaa=dbcbc
babb=d
Right Cayley graph (truncated)
Left Cayley graph (truncated)
Other isomorphic instances
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 308 | ⟨a, b | aababbaa=1⟩ | φ(a) = a, φ(b) = b |
Other anti-isomorphic instances
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 294 | ⟨a, b | aaabbaba=1⟩ | φ(a) = a, φ(b) = b |
| 8 | 334 | ⟨a, b | ababbbba=1⟩ | φ(a) = b, φ(b) = a |